Final answer:
The equation of the line that is perpendicular to y = -2x + 10 and passes through the point (10,7) is y = ½x + 2.
Step-by-step explanation:
To find the equation of the line that is perpendicular to y = −2x + 10 and passes through the point (10,7), first, we determine the slope of the given line. The slope of the given line is -2, so the slope of the perpendicular line will be the negative reciprocal, which is ½. We use the point-slope form of the equation of a line which is y − y1 = m(x − x1), where m is the slope and (x1, y1) is the point through which the line passes. Substituting the slope and the point into the equation, we get y − 7 = ½(x − 10).
Simplifying, we distribute the ½ across the parentheses: y − 7 = ½x − 5. Then we add 7 to both sides to find the y-intercept: y = ½x + 2. This is the equation of the line perpendicular to y = −2x + 10 that goes through (10,7).